How to Make It
In a large saucepan, heat the oil. Generously season the meat with salt and pepper and cook over high heat, stirring occasionally, until browned, 1 to 2 minutes. With a slotted spoon, transfer the meat to a plate.
Add the onions, garlic and a pinch each of salt and pepper to the saucepan and cook, stirring occasionally, until the onions are softened and lightly browned, about 4 minutes. Add the peppers, mushrooms and a pinch each of salt and pepper and cook, stirring occasionally, until the vegetables are softened, about 4 minutes longer.
Stir the meat, beans, tomatoes, Worcestershire sauce and paprika into the saucepan; if the mixture is dry, stir in 1/4 cup of water. Bring to a boil, then reduce the heat to low and simmer for 10 minutes. Remove from the heat and stir in the mayonnaise.
Mound the rice on plates. Top with half of the meat mixture, the American cheese and the remaining meat, then serve.